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      "statement": "# Banach and Tarski: decomposition of point sets into congruent parts\n\nEstablished finite equidecomposition results in Euclidean spaces of dimension at least three, including the result now known as the Banach–Tarski paradox under the set-theoretic assumptions used.\n\n## Scientific scope\n\nThe record is the exact two-author 1924 French paper. It concerns nonmeasurable set-theoretic pieces, not a physically executable cutting process, and does not absorb Hausdorff’s antecedent or later refinements concerning choice principles and piece counts.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\nStefan Banach; Alfred Tarski\n\nThe named authors contributed to this scoped work; individual effort shares and later applications are not assigned by the byline.\n\n\n\n## Original sources\n\n- [Polish Digital Mathematics Library record for Banach–Tarski paper](https://pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-fmv6i1p27bwm)\n- [Banach publication archive entry for joint paper](https://kielich.amu.edu.pl/Stefan_Banach/e-publications.html)\n",
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